If neurons performed the operation of an entire layer, would that make the neural network more effective?
Say, a single neuron could do the function of an entire layer in a network, could that make the network more effective?

That depends what you mean by &quot;more effective&quot;. In terms of number of neurons to achieve the same result, then you should need fewer units. In terms of being able to calculate an end result for any specific problem, then no, because you can generally solve a problem using simpler units by adding more of them.
If this could somehow be done using less resources, it might reduce overall costs. In a biological system, there are possibly overheads per cell in order to maintain it on top of the costs for calculation, so it may be better to do more than the simplest calculation in each cell. Further to that, there may be an optimal amount of processing that each cell could do (this is all conjecture on my part).
In an artifical neural network, the calculations are the only thing being considered, there is no separate overhead per neuron.
There are neural network architectures with complex &quot;sub-units&quot;. Probably the most well known are the recurrent neural network designs for LSTM and gated recurrent units (GRU), plus &quot;skip connections&quot; in residual neural networks. For efficiency these are normally processed in groups per layer with matrix processing functions, but you can also view them as per-neuron complexities.

I am not sure of this- why would complex individual components make the network less effective?

If the complexity was not used, or not really needed, in some of the units, then it would be wasted capacity. In a biological system, this might correspond to maintaining cells larger than they needed to be. In an artificial system, it would mean using memory and CPU to calculate interim values that were not needed for the task at hand.